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Objective Reviews & Commentary - An Engineer's Perspective

September 6, 2011

Noise & Dynamic Range

INTRO: Noise is generally more obvious with headphones than speakers and a relatively common complaint among headphone aficionados. There’s a lot of confusion about sources of noise, specifications, and how to make valid comparisons.

NOISE DEFINED: Technically noise is anything present that’s not related to the desired audio signal. We usually only care about noise within the audible range of 20 hz to 20 Khz. And within that range, the ear is more sensitive to noise at some frequencies than others. The most common audible noise is relatively random in nature and heard as a broadband “hiss”. Low frequency hum at power line frequencies is also sometimes audible. And digital devices, especially computers and mobile phones, can generate noises at specific frequencies that are heard as whines, chirps, clicks, buzzes, etc.

SOURCES OF NOISE: Noise can, and often does, invade the signal chain in audible ways starting at the microphones used during recording. Here are some common sources:

Recordings – Microphone preamps and other gear used during recording often have audible noise. But lots of techniques are used to reduce the audibility of such noise. Noise gating, for example, is used to cut noise when there’s no sound from a given microphone or instrument. Nearly all recordings before the early 80’s were mastered on analog tape which has significant amounts of tape hiss. And even digital recordings can have noise from all the electronics in the signal path. And, of course, vinyl has lots of noise.

DAC – In theory a perfect 16 bit DAC has a 96 dB signal-to-noise ratio but some fall well short of full 16 bit performance. 24 bit DACs often only manage approximately 16 bit performance and the very best reach 21 bit (ENOB) performance. This is especially true of DACs inside a computer. Some DACs also produce significant amounts of their own noise such as as modulation and quantization noise (although these can also be considered forms of distortion as they are only present with a signal).

Headphone Amp – Even a laptop or portable player has a headphone amp in it although it might be built into the same chip as the DAC. Any amplifier adds noise, it’s just a question of if it’s audible or not. Even some fairly expensive stand-alone headphone amps can have significant amounts of noise. They can also further amplify whatever noise is “upstream”.

Noise is Cumulative – While sometimes there’s an obviously dominant source of noise it can just as easily be a little from here and little from there. Noise adds up.

NOISE MEASUREMENTS: There are two basic kinds of noise measurements. One is a an absolute measurement of just the noise and the other is a measurement of the noise relative to some known signal level. The decibel (dB) was partly developed as it more closely follows subjective human hearing. A one dB change in level is about the smallest change most people can detect. A 10 dB change is perceived as being roughly twice as loud (or soft). If Gear A has noise of -80 dBv and Gear B is -70 dBv the second one will have about twice the subjective noise:

Absolute Noise – This is normally measured in microvolts and is the total output with no signal present. It indicates the noise “floor” which is useful from an analytical point of view but less useful for subjective noise evaluation where you’re more concerned about the noise compared to a given realistic listening level. All noise downstream of the volume control is absolute noise.

Relative Noise – This is a more useful measurements as it correlates the noise relative to some known amount of signal. There are decibel units that are referenced to known standards. The most common are dBv and dBu. Noise given in dBv is referenced to a signal of 1 volt RMS and dBu is referenced to 0.775 volts. Both are reasonable listening levels for many full size headphones such as the Sennheiser HD600.

Signal to Noise Ratio (SNR or S/N) – This is a more open ended method where both the noise figure and the reference signal level must be provided for it to be a meaningful number. The correct unit is dBr where the “r” means “relative” but it’s often just given in dB. Unfortunately, many manufactures don’t specify the reference level. When just SNR is specified with no reference you should assume it’s referenced to whatever the absolute maximum output level is for the device--the same as a Dynamic Range measurement. Sadly, that’s often not specified either (see: More Power).

Volts vs dBv vs dBu vs dBr – Measuring noise in volts only works for absolute noise measurements. Measurements in dBv are referenced to 1 volt which makes the math much easier and they’re commonly used in professional audio. 0 dBv = 1 volt. In consumer equipment dBu is more common and referenced to 0.775 volts making the math more awkward. Measurements in dBr can be referenced to anything including each other.

DYNAMIC RANGE: As explained above, Dynamic Range is really the same as the Signal-to-Noise Ratio (SNR) using the maximum possible signal. It’s the ratio between the loudest undistorted output of the device and what’s left over when nothing is playing and is usually a positive number instead of a negative one. The theoretical dynamic range of 16 bit digital audio is 96 dB so that’s often used a benchmark for dynamic range—ideally you don’t want the playback hardware to be worse than the recording format. With higher output gear it’s not uncommon to see dynamic range measurements well above that value so it’s not an unrealistic target. Studies, such as the one conducted by Meyer and Moran, have shown 96+ dB of dynamic range is transparent for any normal listening conditions. The only way to expose the noise floor is to crank up the volume to unrealistic levels. Using a digital (software) volume ahead of a 16 bit DAC and leaving the volume after the DAC cranked way up may expose the 16 bit noise floor. In these applications 110 dB of dynamic range should be sufficient to keep the noise below ambient levels.

VOLUME SETTING: There are some interesting twists with volume settings some of which are not intuitive:

Upstream Noise - Any noise that’s “upstream” of the volume control will be more audible as you turn the volume up assuming the music doesn’t mask it. The absolute noise is worse at higher volume settings but the SNR stays about the same because you’re also increasing the signal by the same amount as you turn up the volume.

Amplifier Noise – Depending on where the volume control is located within the gear it may or may not significantly alter the noise. A digital volume control, for example, will only affect the noise in the recording itself (and not change SNR at all). Interestingly some devices with analog volume controls have the most noise at half volume—such as the FiiO E9. This is usually because you’re hearing the Johnson Noise of the volume control itself where half volume is the worst case situation. This is typical when the volume control is before the gain stage. When the volume is after the gain stage, most everything becomes Upstream Noise (see above) and is reduced at lower volume settings.

Fixed Noise – Amps have a certain amount of noise that’s present at any volume setting. This is usually noise that’s from the circuitry after the volume control and, in a properly designed amp, it’s entirely possible to have it always be inaudible.

WORST CASE NOISE AUDIBILITY: Some define audible noise as anything you can hear under worst case conditions—i.e. nothing playing, the worst case volume and gain settings, a very quiet room, and using extremely sensitive headphones. An easily accepted guideline is –96 dB un-weighted referenced to a realistic maximum listening level (see Dynamic Range above) as that’s the maximum dynamic range of 16 bit digital audio. So whatever level produces around 110 dB peak SPL (see my Power article) should be the reference value and as long as the noise is about 96 dB below that it will be entirely inaudible. That’s achievable with less sensitive headphones but difficult with ultra sensitive IEMs. Some examples

HD600 – 2.3 V for 110 dB gives 36 uV or –88 dBv of noise

GRADO SR80 – 0.7 V for 110 dB gives 11 uV or –99 dBv of noise

U.E. TripleFi 10 – 0.1 V for 110 dB gives 1.6 uV or –116 dBv of noise

PRACTICAL NOISE AUDIBILITY: In reality, testing shows that 85 dB below 110 dB SPL is sufficiently quiet for most people (noise of 25 dB SPL). That puts the limit at –105 dBv, (-102.8 dBu) or 5.6 uV for sensitive IEMs. With the most sensitive IEMs in a really quiet room someone might still hear some noise at that level, but being realistic, it’s likely “good enough”. If you want to be assured of silence with even the most sensitive IEMs, aim for –110 dBv (-107.8 dBu).

NOISE & GAIN: Headphone amps have varying amounts of gain--the maximum amount they can amplify the input signal. Some have multiple gain settings. The higher the gain the more they will amplify upstream noise. And, typically, the higher the gain the higher their own noise. This is one reason you ideally want to use the lowest amount of gain required. See: All About Gain

Noise dBv Volume 100% – The O2 measures –112 dBv un-weighted and –115 dBv A-Weighted. This is well below the –105 dBv guideline and means the O2 will be silent in use.

SNR Referenced to Full Output – The O2 referenced to 7 volt RMS (full output) measures –130 dBr unweighted and –133 dBr A-Weighted. These numbers are extremely impressive but also unrealistic for most users who will never need even close to 7 Vrms of output.

HEADPHONE SENSITIVITY: Headphones vary widely in their sensitivity. Many assume a headphone that’s 10 dB more sensitive will make the SNR 10 dB worse but that’s often not true. As headphones become more sensitive, you need less gain, and/or use lower volume settings. Both of those typically lower noise So the ratio of the signal to the upstream noise, and hence the SNR, stays about the same. Only fixed noise (see above) is directly related to the headphone sensitivity. Johnson Noise from the volume control can complicate this a bit but as headphones become more sensitive the fixed noise becomes much more important. See Noise Audibility Worst Case above for examples of three different headphones.

NOISE SPECTRUMS: Sometimes you will see a spectrum graph for noise measurements. The approximate “noise floor” in these graphs is much lower than the actual noise specification. In the graph to the right the overall noise is about –112 dBv but the noise floor is down around –150 dBv in the graph. This huge difference is because the –112 dB number is the sum of all the noise from 20hz to 20 Khz. Think of spreading a cup of sugar out across the floor. It would barely change the height of the floor. But if you gather all the sugar up in a measuring cup, you can know how much total sugar there is—much like the noise measurements shown in the boxes in the graph. Click the graph for a larger version.

NOISE BANDWIDTH AND WEIGHTING: Typically noise is the sum of all energy within the audio band. Ideally the bandwidth is specified for un-weighted measurements. A-Weighting is often used which adjusts the measurement for the relative sensitivity of the ear at different frequencies and also limits the bandwidth. Another weighting standard is ITU-R 468. For gear that’s prone to a lot of out-of-band ultrasonic noise, such as Class-D amplifiers and digital equipment, a wideband noise measurement up to about 100 Khz can also sometimes be useful in addition to weighted/limited measurements.

COMPARING NOISE MEASUREMENTS: You can only directly compare noise measurements given in dBu, dBv, or dBr at the same reference level. And they must use a similar bandwidth and all be either unweighted or weighted the same way. Otherwise, you can’t compare the numbers without at least doing some math and sometimes you can’t compare them at all. Here are some examples:

RMAA – Unfortunately RMAA has no concept of absolute levels. So it can’t calculate noise levels referenced to any known value. It attempts to calculate dynamic range against ) dBFS (the clipping level of the DAC itself) but even that is subject to wide variations in the device settings (i.e. volume, “record” level, etc.), calibration settings, etc. Basically RMAA noise measurements are nearly worthless and the noise of the PC sound hardware might be worse than whatever you’re trying to measure anyway. Some RMAA results are comparatively arbitrary and this is one of them.

dBv to dBr – If Gear A has a noise spec of –100 dBv and Gear B is –108 dBr (ref 10 Vrms) at first glance B looks to be a significant 8 dB quieter. But A is referenced to 1 V and B 10 V. The difference is 20*Log(10/1) = 20 dB. So B is really 20 dB worse reference to 1V or only –88 dBv. See Generic Conversions below.

dBu to dBv – These are close. To convert from dBv to dBu the noise is 2.2 dB worse. To convert the other way it’s 2.2 dB better.

dBr (400 mV) to dBv – I updated my own noise measurements from dBr referenced to 400 mV to dBv (referenced to 1 volt). To convert the old 400 mV measurement to dBv the noise improves by 8 dB. To convert the other way, it’s worse by 8 dB.

Generic Conversions – The generic math for the amount to add or subtract is 20 * Log( Vref1 / Vref2). The lower the reference voltage the worse the noise figure. Noise can also be referenced to power instead of voltage. In that case it’s 10 * Log ( Pref1 / Pref2 ).

dBv to Volts = antilog( dBv / 20 )

-96 dB in Volts = antilog ( –96/20 ) = 16 uV ( 0.000016 volts)

Volts to dBv = 20 * log ( Vnoise )

Weighting Comparisons – It’s impossible to accurately compare different weighting or weighted vs un-weighted as it depends on the frequency distribution of the noise. An amp with a lot of hum, for example, will have a proportionately lower weighted measurement than one with only uniform hiss. In general, however, expect an A-Weighted measurement to be about 3 to 6 dB better than an un-weighted measurement.

SOURCE IMPEDANCE:Johnson Noise is often a dominant source of noise in headphone amps and preamps. And it’s proportional to the impedance of the input circuitry which includes the source. The higher the source impedance, the higher the noise. So, for example, a given headphone amp might be dead silent when driven from a source with a 100 ohm impedance, but using a source with a 10K impedance could easily produce audible noise. In this case the noise you’re hearing is really coming from the upstream source not the amp.

MEASURING NOISE: Because noise measurements are a sum of the noise across the audio band, and extremely low in value, they’re tricky to measure accurately. The best high-end 24 bit PC sound hardware may have a low enough noise floor, but often cannot accept the full output of the device being tested. And more significant, PC sound hardware has no way to set or measure absolute levels—i.e. measurements in volts, dBv, etc. Very few Digital Multi Meters (DMMs) have the resolution and low enough internal noise to measure accurately down to a few microvolts of AC from 20 hz to 20 Khz. It is, in theory, possible to temporarily calibrate a 24 bit soundcard using a known accurate meter and suitable test tones. But it’s tricky to do accurately and apply to whatever software is being used. The source impedance is also an issue. Manufactures tend to short circuit the inputs for the best noise number, a more realistic test is to use a shunt resistance equal to the output impedance of a typical source. If you try to use a real source, its noise will also be included in the measurement (as with RMAA). Also, when measuring a source with a DAC it’s necessary to use a very low level test signal as DACs shut off completely giving an unrealistic noise value if there is nothing to play. A proper audio analyzer can remove the low level signal from the measurement leaving just the noise.

RMAA MEASUREMENTS: Even if you somehow calibrate the levels, you still don’t know what RMAA is doing internally. It’s a magic “black box” with no credible documentation about how it arrives at its final numbers. What bandwidth is being used? Is the result weighted or un-weighted? Plus the unknown output noise of the RMAA sound hardware is included in the measurement by design. Ultimately, the best way to make noise measurements is with an audio analyzer such as those from Audio Precision and Prism Sound.

BOTTOM LINE: Noise of around –105 dBv (referenced to 1 volt) will nearly always be inaudible. Noise around -95 dBv is probably “good enough” for many. Noise referenced to other values must be converted to dBv or another consistent reference before it can be fairly compared. RMAA values are nearly useless because RMAA has no concept of absolute levels. It can only provide dynamic range and it often gets even that wrong because it’s difficult to set the levels properly without proper instrumentation.

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comments:

If you're talking about what happens when an amp reaches its output limit, I talk about that more in the More Power? article. But, as a rule, a properly performing amp will clip in much the same way regardless of which limit is reached first.

In general Maverick, yes, you're correct. I should probably make that more clear. Absolute noise, and fixed noise become more of a problem as the headphone sensitivity goes up. Everything else is relative to the signal.

That's why I designed the O2 as I did. I wanted the absolute and fixed noise to be as low as possible to assure even BA IEMs were silent.

Thanks STM, the Myths Workshop is great for many reasons! The link to the edited video and the related sound files are in my Subjective vs Objective article.

To answer your question there are some subjective differences in sources of noise--much like white vs pink noise. White noise sounds "brighter" and pink noise (similar to 1/f noise) sounds more "dull" because of the octave-to-octave spectral energy difference.

The idea behind weighting noise measurements is to automatically correct for different types of noise. The idea is say -70 dB A-weighted will be similarly objectionable from a subjective perspective regardless of what all it's made up of. So Gear A might be -70 dB mainly from johnson noise and Gear B might be -70 dB mainly from 1/f noise, but the subjective overall level would be roughly the same. I should probably make it more clear in the article that you're better off comparing weighted measurements if they're available for that reason.

HS, it's more complex than that but you bring up a good point. If you look at the O2's schematic, for example, you'll see it has about 200 ohms in series with the input and 10,000 ohms in parallel. The 10,000 ohms determines the input impedance. But the Johnson Noise is the 200 ohms + the output impedance of the source. Only if the source is over about 10,000 ohms will the O2's own input impedance dominate and that's not very likely as a 10,000 ohm output impedance would make for a very poor source.

Perhaps more to your point, the series resistance can make a difference in some amps as it's not uncommon to see values of 1000 ohms or more. The series input resistance can be the dominant source of Johnson Noise if the source's output impedance is much lower.

But it gets more complex still as below some level of Johnson Noise other sources of noise start to dominate (such as the op amp's current and voltage noise). In the case of the O2 everything else is so quiet the source can easily be the dominant noise source. In an amp that's much noisier on its own, the source impedance will have less impact on the total noise level.

I'll consider editing the article a bit to make it more clear. I'm trying to cover the main points without making too many eyes glaze over. Many of these sub-topics, like Johnson Noise, are entire chapters in a book.

About distorsion...how does intermodulation distorsion sound ? . How would you rate a device which features 0.522 IMD+Noise measurement driving a 32Ohm AKGs. Is there a huge audible gap between that figure and 0.092 ?

As usual is really great the chance to learn about audio to cope better with all the marketing gimmicks.

@Gonzalo, what device has 0.522% IMD+N? That's fairly high IMD. Is that an RMAA number? If so, it's really hard to know what's going on (see my February RightMark Audio Analyzer article).

I'm working on an article about distortion. Numbers that high (0.5%) can often be audible. My guideline is 0.01% - 0.05%.

@bithead, if you're happy with your laptop I'd probably not try any upgrades. If you're really curious, the $20 FiiO E5 is an inexpensive to find out and would work well with both those headphones. For noise samples, check the Audio Myths Workshop links in the Subjective vs Objective debate article. For evaluating noise, playing a file with something like a single tone at -90 dBFS or -100 dBFS is best as playing a file with nothing (or hitting the pause button) causes most DACs to mute or shut down. I'll look into offering a sample sound file (sound files are difficult to host due to bandwidth issues).

It was for an smartphone that was RMAAed at Gsmarena.com it seems that these folks should be taught about RMAA. it's the only smartphone review site that tries to measure audio output. Unfortunately their results are really odd except for one thing: iPhone 4 always destroys any other smartphone in the sound area.

fyi FIIO just released an upgraded version of the E5 dubbed E6 and it seems to get rid of the bass roll off.

RMAA, if you're aware of its problems (unfortunately most don't seem to be) can be better than no audio measurements at all. I'm not surprised about the iPhone. The iPod Touch 3G and 4G measure very well. And, AFAIK, Apple used essential the same sound hardware in the iPhone. My iPod Touch 3G measures much better than a few different Android and Nokia smartphones I've tested. If Gsmarena is at least being consistent, and knows about setting levels correctly, you can probably at least get some relative idea between the phones they've tested.

Hi! I really like your blog, it is amazing. I think you should cover in the next article, that the biggest noise source is the DAC itself. I was playing with a PCM2702 theese days, and found out that the signal coming from the IC itself is just horrible. The poor Sigma-Delta converters 1 bit output ends has so much noise, that i wasn't able to set the scope to measure (without averaging).What i'm sayig is I would really like an article from you with the Anti-Aliasing filters.

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